Studies of the interface motion and the signal propagation mechanism in the bidomain model

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610028
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: The University of Tokyo
• Principal Investigator: Matano Hiroshi 東京大学, 大学院数理科学研究科, 教授 (40126165)
• Research Collaborator: MORI Yoichiro ミネソタ大学, 数学科, 准教授
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: バイドメインモデル / 平面波 / 安定性 / フランク図形 / 擬微分方程式 / 定性的理論 / 非線形問題

Outline of Final Research Achievements

In this research project, we made a detailed study of the stability of planar traveling waves of the bidomain Allen-Cahn equation.
First, we analyzed the linear stability of planar traveling waves using the spectral information. We revealed the relation between the stability of the planar wave under long-wavelength perturbations and the concavity-convexity properties of the Frank diagram. We also derived remarkable results on the linear stability under medium-wavelength perturbations. Next we proved that linear stability implies nonlinear stability.
Our work gives the first successful results on the stability analysis of bidomain models.

Free Research Field

非線形解析学